Back to Ganita Prakash: Class 7 Mathematics, Par...BackConcept

Naming Congruent Triangles

Why the order of letters in a congruence statement matters, and how to write one correctly.

8 micro-lessons

Preview · progress not saved — Chapter 1 is free

The Wrong Way to Overlap

A congruence written in the wrong order matches the wrong sides.

Let's return to the rectangle $ABCD$ split by the diagonal $BD$ . We know the two resulting triangles, $\Delta ABD$ and $\Delta CDB$ , are congruent because all three of their corresponding side lengths match (the SSS condition).

1 / 3

Which Vertex Meets Which

Two congruent triangles with matching sides marked by ticks.

$Naming Congruent Triangles$

Click to zoom

Corresponding vertices match up so that the equal sides perfectly overlap.

Reading a Congruence Statement

What the order of letters in ABC congruent to XYZ actually says.

When we write $\Delta ABC \cong \Delta XYZ$ , the order of the letters isn't random. It packs three distinct claims into one statement: the first vertex of the first triangle corresponds to the first vertex of the second triangle, the second to the second, and the third to the third.

1 / 4

Correspondence Rules Card

How to write, check and rewrite a congruence statement.

The Symbol

≅

The Meaning

First vertex matches first, second matches second, third matches third. The order MUST place equal sides opposite each other.

The Rewriting Rule

Δ A BC ≅ Δ X Y Z

, you can start from any vertex as long as both names shift together.
Rotations:

BC A \to Y ZX

and

C A B \to ZX Y

. Reversing yields 3 more, giving 6 valid ways in total!

Example Substitution

From

Δ H EN ≅ Δ B I G

, we immediately extract:

$H E = B I$
$EN = I G$
$N H = GB$

Fixing the Rectangle Statement

Finding the correct correspondence for the two triangles in rectangle ABCD.

Problem.
Express the congruence of the two triangles formed by the diagonal $BD$ in rectangle $ABCD$ .

1 / 6

Match the Corresponding Parts

Pair up sides and angles using a given congruence statement.

NoteGiven that ΔHEN is congruent to ΔBIG, match the corresponding parts. Read the order of the letters in the statement, not your guess of the appearance!

0 of 6 connected

Terms

Definitions

Is This Statement Correct?

Decide which congruence statements are written correctly.

1 / 4

If you are given that $\Delta ABC \cong \Delta XYZ$ , is the statement $\Delta ACB \cong \Delta XYZ$ also correct?

← previousThree Sides Are Enough next →Two Sides And The Angle Between

The Wrong Way to Overlap

A congruence written in the wrong order matches the wrong sides.

1 / 3

Reading a Congruence Statement

What the order of letters in ABC congruent to XYZ actually says.

1 / 4

Fixing the Rectangle Statement

Finding the correct correspondence for the two triangles in rectangle ABCD.

Problem.
Express the congruence of the two triangles formed by the diagonal $BD$ in rectangle $ABCD$ .

1 / 6

Is This Statement Correct?

Decide which congruence statements are written correctly.

1 / 4

If you are given that $\Delta ABC \cong \Delta XYZ$ , is the statement $\Delta ACB \cong \Delta XYZ$ also correct?